Question

How much should the pressure be increased in order to decrease the volume of a gas by 5%"at a constant temperature

Answer 1

Given:

A gas at a constant temperature.

To find:

How much should the pressure be increased in order to decrease the volume of a gas by 5%"at a constant temperature

Solution:

From given, we have,

A gas at a constant temperature.

According to Boyle's law  ("The pressure of a given mass of an ideal gas is inversely proportional to its volume at a constant temperature.")

P₁V₁ = P₂V₂,

V₁ = V and V₂ = 0.95V  (5% = 1 - 5/100 = 1 - 0.05 = 0.95)

⇒ P₁ × V = P₂ × 0.95V

⇒ P₁ = P₂ × 0.95

or P₂ = P₁/0.95 = 1.0526P₁

Increase in pressure

= P₂ - P₁

= 1.0526 P₁ − P₁ = 0.0526P₁ = 5.26% of P₁

∴ The pressure should be increased by 5.26% in order to decrease the volume of a gas by 5% at a constant temperature.

Answer 2

Answer:

5.26 %

Explanation:

Let P1 = 1 atm and V1 = 1 L

now , P2 = ? and V2 = 1 - 5 % ( according to question )

so , V2 = 1 - 5/100 = 0.95 L

from Boyle's law : P1V1 = P2V2 => P2 = P1V1 / V2

P2 = 1 × 1 / 0.95 = 1.0526 atm

Increase in pressure = P2 - P1 = 1.0526 - 1 = 0.0526 atm

Now percentage increase = 0.0526 × 100 % = 5.26 %